Area:
Area can be defined as the surface measured inside the boundary of a 2–dimensional plane objects like triangle, circle, rectangle, square,… In the following diagrams, red surface denotes the area.
Area is measured in terms of unit squares (unit centimeter squares or unit meter squares)
Standard unit of area of plane figures is a square centimeter (cm2) or square meter(m2)
Square centimeter (cm2) is the area of planar region bounded by a square of side one centimeter.
Square meter (m2) is the area of planar region bounded by a square of side one meter.
Area of Plane closed figures:
Area of a triangle= $\frac{1}{2}$ x b x h square units where b is the base and h is the height
Area of rectangle = l x w square units where l is the length and w is the width
Area of trapezoid =$\frac{1}{2}$(a +b) h square units where a and b are the length of the sides of the trapezoid and h is the vertical height
Area of square= a2 square units where a is the length of the side of the square
Area of parallelogram= b x h square units where b and h are base and height of the parallelogram
Area of circle = $\pi$ x r2 square units where r is the radius of the circle
Example problems :
1. Calculate the area of the trapezoid with their sides as 5 inches and 3 inches and the height is 4 inches.
Given : a = 5 inches, b = 3 inches, h =4 inches
Area of the trapezoid =$\frac{1}{2}$(a +b) h square units
= $\frac{1}{2}$(5 + 3) x 4
= $\frac{1}{2}$ x 8 x 4
= 16 square inches
2. Calculate the area of the circle with radius 7 cm.
Given: radius = 7 cm
Area of the circle= $\pi$ x r2 square units
= $\pi$ x 72
= 49$\pi$ cm2
3. Calculate the area of the parallelogram with base 5 inches and height 7 inches
Given: base= 5 inches and height =7 inches
Area of parallelogram= b x h square units
= 5 x 7
= 35 square inches
Perimeter
Perimeter is the total length required to make the the boundary of a 2 – dimensional plane objects such as triangle, circle, rectangle, square,… The black line denotes the perimeter.
To find the perimeter of any plane figures, we have to add the length of each side.
Example:
Calculate the perimeter of a triangle with sides measuring 4 centimeters, 5 centimeters and 6 centimeters.
Perimeter of the triangle = 4 + 5 + 6
= 15 cm
A rectangle has a length of 6 centimeters and a width of 3 centimeters. Calculate the perimeter.
Solution 1: P = 6 cm + 6 cm + 3 cm + 3 cm = 18 cm
Solution 2: P = 2(6 cm) + 2(3 cm) = 12 cm + 6 cm = 18 cm
Perimeter of plane surfaces with equal sides:
To find the perimeter of plane surfaces with equal sides, count the number of sides and multiply it with the length of the side.
Example:
- Find the perimeter of a square with each side measuring 3 inches
A square has 4 sides
Perimeter of the square = 4 x side
= 4 x 3
=12 inches
2. Find the perimeter of an equilateral triangle with each side measuring 5 centimeters.
A triangle has three sides
perimeter of an equilateral triangle= 3 x 5
= 15 centimeters
3. Find the perimeter of the following figure
AB = FE + DC
= 5 + 5 = 10 cm
BC = AF + ED
= 4 + 4 = 8 cm
Perimeter = AB + BC + CD + DE + EF + FA
= 10 + 8 + 5 + 4 + 5 + 4
= 36 cm
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